The Cauchy problem for improper affine spheres and the Hessian one equation |
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| Authors: | Juan A Aledo Rosa M B Chaves José A Gá lvez |
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| Institution: | Departamento de Matemáticas, Universidad de Castilla-La Mancha, 02071 Albacete, Spain ; Instituto de Matemática e Estatística, Universidade de São Paulo, 05315-970 São Paulo-SP, Brazil ; Departamento de Geometría y Topología, Universidad de Granada, 18071 Granada, Spain |
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| Abstract: | We give a conformal representation for improper affine spheres which is used to solve the Cauchy problem for the Hessian one equation. With this representation, we characterize the geodesics of an improper affine sphere, study its symmetries and classify the helicoidal ones. Finally, we obtain the complete classification of the isolated singularities of the Hessian one Monge-Ampère equation. |
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